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  2. Polynomial regression - Wikipedia

    en.wikipedia.org/wiki/Polynomial_regression

    Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression. [1]

  3. Curve fitting - Wikipedia

    en.wikipedia.org/wiki/Curve_fitting

    A line will connect any two points, so a first degree polynomial equation is an exact fit through any two points with distinct x coordinates. If the order of the equation is increased to a second degree polynomial, the following results: = + +. This will exactly fit a simple curve to three points.

  4. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    Sometimes the word "order" is used with the meaning of "degree", e.g. a second-order polynomial. However, where the "degree of a polynomial" refers to the largest degree of a non-zero term of the polynomial, more typically "order" refers to the lowest degree of a non-zero term of a power series.

  5. Linear least squares - Wikipedia

    en.wikipedia.org/wiki/Linear_least_squares

    Optimal instruments regression is an extension of classical IV regression to the situation where E[ε i | z i] = 0. Total least squares (TLS) [6] is an approach to least squares estimation of the linear regression model that treats the covariates and response variable in a more geometrically symmetric manner than OLS. It is one approach to ...

  6. Regression analysis - Wikipedia

    en.wikipedia.org/wiki/Regression_analysis

    Second, in some situations regression analysis can be used to infer causal relationships between the independent and dependent variables. Importantly, regressions by themselves only reveal relationships between a dependent variable and a collection of independent variables in a fixed dataset.

  7. Polynomial interpolation - Wikipedia

    en.wikipedia.org/wiki/Polynomial_interpolation

    Hermite interpolation problems are those where not only the values of the polynomial p at the nodes are given, but also all derivatives up to a given order. This turns out to be equivalent to a system of simultaneous polynomial congruences, and may be solved by means of the Chinese remainder theorem for polynomials.

  8. Taylor's theorem - Wikipedia

    en.wikipedia.org/wiki/Taylor's_theorem

    For a smooth function, the Taylor polynomial is the truncation at the order of the Taylor series of the function. The first-order Taylor polynomial is the linear approximation of the function, and the second-order Taylor polynomial is often referred to as the quadratic approximation. [1]

  9. Local regression - Wikipedia

    en.wikipedia.org/wiki/Local_regression

    Local regression or local polynomial regression, [1] also known as moving regression, [2] is a generalization of the moving average and polynomial regression. [3] Its most common methods, initially developed for scatterplot smoothing, are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing), both pronounced / ˈ l oʊ ɛ s / LOH-ess.